405 research outputs found
Randomized Polar Codes for Anytime Distributed Machine Learning
We present a novel distributed computing framework that is robust to slow
compute nodes, and is capable of both approximate and exact computation of
linear operations. The proposed mechanism integrates the concepts of randomized
sketching and polar codes in the context of coded computation. We propose a
sequential decoding algorithm designed to handle real valued data while
maintaining low computational complexity for recovery. Additionally, we provide
an anytime estimator that can generate provably accurate estimates even when
the set of available node outputs is not decodable. We demonstrate the
potential applications of this framework in various contexts, such as
large-scale matrix multiplication and black-box optimization. We present the
implementation of these methods on a serverless cloud computing system and
provide numerical results to demonstrate their scalability in practice,
including ImageNet scale computations
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Error-corrected quantum repeaters with GKP qudits
The Gottesman-Kitaev-Preskill (GKP) code offers the possibility to encode
higher-dimensional qudits into individual bosonic modes with, for instance,
photonic excitations. Since photons enable the reliable transmission of quantum
information over long distances and since GKP states subject to photon loss can
be recovered to some extent, the GKP code has found recent applications in
theoretical investigations of quantum communication protocols. While previous
studies have primarily focused on GKP qubits, the possible practical benefits
of higher-dimensional GKP qudits are hitherto widely unexplored. In this paper,
we carry out performance analyses for three quantum repeater protocols based on
GKP qudits including concatenations with a multi-qudit quantum polynomial code.
We find that the potential data transmission gains for qudits are often
hampered by their decreased GKP error-correcting capabilities. However, we also
identify parameter regimes in which having access to an increased number of
quantum levels per mode can enhance the theoretically achievable secret-key
rate of the quantum repeater. Some of our protocols share the attractive
feature that local processing and complete error syndrome identification are
realizable without online squeezing. Provided a supply of suitable multi-mode
GKP states is available, this can be realized with a minimal set of passive
linear optical operations, even when the logical qudits are composed of many
physical qudits.Comment: 19+11 pages, 6+4 figures. Comments welcom
Single-Frequency Network Terrestrial Broadcasting with 5GNR Numerology
L'abstract è presente nell'allegato / the abstract is in the attachmen
Easily decoded error correcting codes
This thesis is concerned with the decoding aspect of linear block error-correcting codes. When, as in most practical situations, the decoder cost is limited an optimum code may be inferior in performance to a longer sub-optimum code' of the same rate. This consideration is a central theme of the thesis.
The best methods available for decoding short optimum codes and long B.C.H. codes are discussed, in some cases new decoding algorithms for the codes are introduced.
Hashim's "Nested" codes are then analysed. The method of nesting codes which was given by Hashim is shown to be optimum - but it is seen that the codes are less easily decoded than was previously thought.
"Conjoined" codes are introduced. It is shown how two codes with identical numbers of information bits may be "conjoined" to give a code with length and minimum distance equal to the sum of the respective parameters of the constituent codes but with the same number of information bits. A very simple decoding algorithm is given for the codes whereby each constituent codeword is decoded and then a decision is made as to the correct decoding. A technique is given for adding more codewords to conjoined codes without unduly increasing the decoder complexity.
Lastly, "Array" codes are described. They are formed by making parity checks over carefully chosen patterns of information bits arranged in a two-dimensional array. Various methods are given for choosing suitable patterns. Some of the resulting codes are self-orthogonal and certain of these have parameters close to the optimum for such codes. A method is given for adding more codewords to array codes, derived from a process of augmentation known for product codes
Computer Aided Verification
This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book
Fast Decoding of Interleaved Linearized Reed-Solomon Codes and Variants
We construct s-interleaved linearized Reed-Solomon (ILRS) codes and variants
and propose efficient decoding schemes that can correct errors beyond the
unique decoding radius in the sum-rank, sum-subspace and skew metric. The
proposed interpolation-based scheme for ILRS codes can be used as a list
decoder or as a probabilistic unique decoder that corrects errors of sum-rank
up to , where s is the interleaving order, n the
length and k the dimension of the code. Upper bounds on the list size and the
decoding failure probability are given where the latter is based on a novel
Loidreau-Overbeck-like decoder for ILRS codes. The results are extended to
decoding of lifted interleaved linearized Reed-Solomon (LILRS) codes in the
sum-subspace metric and interleaved skew Reed-Solomon (ISRS) codes in the skew
metric. We generalize fast minimal approximant basis interpolation techniques
to obtain efficient decoding schemes for ILRS codes (and variants) with
subquadratic complexity in the code length. Up to our knowledge, the presented
decoding schemes are the first being able to correct errors beyond the unique
decoding region in the sum-rank, sum-subspace and skew metric. The results for
the proposed decoding schemes are validated via Monte Carlo simulations.Comment: submitted to IEEE Transactions on Information Theory, 57 pages, 10
figure
Emerging Approaches to DNA Data Storage: Challenges and Prospects
With the total amount of worldwide data skyrocketing, the global data storage demand is predicted to grow to 1.75 × 1014GB by 2025. Traditional storage methods have difficulties keeping pace given that current storage media have a maximum density of 103GB/mm3. As such, data production will far exceed the capacity of currently available storage methods. The costs of maintaining and transferring data, as well as the limited lifespans and significant data losses associated with current technologies also demand advanced solutions for information storage. Nature offers a powerful alternative through the storage of information that defines living organisms in unique orders of four bases (A, T, C, G) located in molecules called deoxyribonucleic acid (DNA). DNA molecules as information carriers have many advantages over traditional storage media. Their high storage density, potentially low maintenance cost, ease of synthesis, and chemical modification make them an ideal alternative for information storage. To this end, rapid progress has been made over the past decade by exploiting user-defined DNA materials to encode information. In this review, we discuss the most recent advances of DNA-based data storage with a major focus on the challenges that remain in this promising field, including the current intrinsic low speed in data writing and reading and the high cost per byte stored. Alternatively, data storage relying on DNA nanostructures (as opposed to DNA sequence) as well as on other combinations of nanomaterials and biomolecules are proposed with promising technological and economic advantages. In summarizing the advances that have been made and underlining the challenges that remain, we provide a roadmap for the ongoing research in this rapidly growing field, which will enable the development of technological solutions to the global demand for superior storage methodologies
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DISTRIBUTED LEARNING ALGORITHMS: COMMUNICATION EFFICIENCY AND ERROR RESILIENCE
In modern day machine learning applications such as self-driving cars, recommender systems, robotics, genetics etc., the size of the training data has grown to the point that it has become essential to design distributed learning algorithms. A general framework for the distributed learning is \emph{data parallelism} where the data is distributed among the \emph{worker machines} for parallel processing and computation to speed up learning. With billions of devices such as cellphones, computers etc., the data is inherently distributed and stored locally in the users\u27 devices. Learning in this set up is popularly known as \emph{Federated Learning}. The speed-up due to distributed framework gets hindered by some fundamental problems such as straggler workers, communication bottleneck due to high communication overhead between workers and central server, adversarial failure popularly know as \emph{Byzantine failure}. In this thesis, we study and develop distributed algorithms that are error resilient and communication efficient.
First, we address the problem of straggler workers where the learning is delayed due to slow workers in the distributed setup. To mitigate the effect of the stragglers, we employ \textbf{LDPC} (low density parity check) code to encode the data and implement gradient descent algorithm in the distributed setup. Second, we present a family of vector quantization schemes \emph{vqSGD} (vector quantized Stochastic Gradient Descent ) that provides an asymptotic reduction in the communication cost with convergence guarantees in the first order distributed optimization. We also showed that \emph{vqSGD} provides strong privacy guarantee. Third, we address the problem of Byzantine failure together with communication-efficiency in the first order gradient descent algorithm. We consider a generic class of - approximate compressor for communication efficiency and employ a simple \emph{norm based thresholding} scheme to make the learning algorithm robust to Byzantine failures. We establish statistical error rate for non-convex smooth loss. Moreover, we analyze the compressed gradient descent algorithm with error feedback in a distributed setting and in the presence of Byzantine worker machines. Fourth, we employ the generic class of - approximate compressor to develop a communication efficient second order Newton-type algorithm and provide rate of convergence for smooth objective. Fifth, we propose \textbf{COMRADE} (COMmunication-efficient and Robust Approximate Distributed nEwton ), an iterative second order algorithm that is communication efficient as well as robust against Byzantine failures. Sixth, we propose a distributed \emph{cubic-regularized Newton } algorithm that can escape saddle points effectively for non-convex loss function and find a local minima . Furthermore, the proposed algorithm can resist the attack of the Byzantine machines, which may create \emph{fake local minima} near the saddle points of the loss function, also known as saddle-point attack
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